Space of modular forms of level 33, weight 6, and Character 33.e

• Label: 33.6.e
• Level: $33$
• Weight: $6$
• Character orbit: 33.e
• Rep. character: $\chi_{33}(4,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $40$
• Newform subspaces: $2$
• Sturm bound: $24$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	33.e (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(24\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(33, [\chi])\).

	Total	New	Old
Modular forms	88	40	48
Cusp forms	72	40	32
Eisenstein series	16	0	16

Trace form

\( 40 q + 4 q^{2} - 116 q^{4} - 44 q^{5} - 72 q^{6} - 474 q^{7} - 548 q^{8} - 810 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(33, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
33.6.e.a	$33$	$6$	33.e	11.c	$5$	$20$	$5$	$5.293$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(-2\)	\(-45\)	\(-33\)	\(-335\)	$2^{4}\cdot 11^{2}$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\beta _{1}+\beta _{7})q^{2}-9\beta _{9}q^{3}+(-\beta _{6}+\cdots)q^{4}+\cdots\)
33.6.e.b	$33$	$6$	33.e	11.c	$5$	$20$	$5$	$5.293$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(6\)	\(45\)	\(-11\)	\(-139\)	$2^{4}\cdot 11^{2}$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\beta _{5}+\beta _{6})q^{2}+9\beta _{7}q^{3}+(-12+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(33, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(33, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)